the physics behind how modern archery bows work

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I’ve spent about 2 hours watching videos on YouTube to understand how bows work but I’m getting more videos that are pitched at comparisons between different modern bows or how to shoot videos.

What I don’t understand is how a compound bow or springed bow is able to make a small person shoot at higher power. In my physics mind, I understand that cams and springs provide leverage. But the force applied to build potential energy is the same direction as the arrow being fired, so how does the arrow have more power?

if I’m using a seesaw analogy, I’m charging potential energy with the end of the seesaw, when I jump off, the far end of the seesaw still has the same distance to the fulcrum

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Anonymous 0 Comments

So the thing about a bows limbs is that they have to accelerate their own weight as well as the arrow. And decelerate too which shocks the limbs and can damage them if they are undersized, or if you dry fire a bow and the arrow isn’t there to absorb some energy.

The cams on a bow allow for the use of higher stiffness materials that only need to bend a short distance for the same draw length compared to a recurve. Less distance the limb accelerates means less energy wasted in the limbs. You can get over this somewhat with just using a really tall bow with high stiffness as the limbs don’t have to bend as much for the same draw, but the compound bow is much more compact.

This also ties into the weight of an arrow. A lighter weight arrow travels faster and flatter however using lighter weight arrows means that the bow limbs use more energy accelerating themselves than the arrow. The overall kinetic energy in a lightweight arrow is less compared to a heavier weight arrow. Since the compound bows limbs are lighter with a short travel distance they work more efficiently at transferring energy to the arrow. You’ll also see compound bow arrow weights tend to be lighter. You are trading off some of the increase in power for a slightly more inefficient arrow that travels faster.

The cams also allow the limbs to be placed more horizontal instead of vertical. That means instead of accelerating forward and yoinking the whole bow forward out of your hands the force is mostly up and down, cancelling. There’s shock on the frame, but the frame is built to handle it and there’s much less force trying to propel the bow forward after a shot. You’ll notice that the more powerful a compound is the more horizontal the limbs that bend tend to get.

Lastly the cams are shaped so that instead of force building up to a peak, the force lets off at full draw. This doesn’t add more power directly, but it means that after the initial hard pull it’s much easier to hold back for aiming and makes it much more usable since you aren’t shaking trying to keep it drawn.

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